American Institute of Mathematical Sciences

• Previous Article
Pointwise bounds for the Green's function for the Neumann-Laplace operator in $\text{R}^3$
• KRM Home
• This Issue
• Next Article
The fragmentation equation with size diffusion: Small and large size behavior of stationary solutions
doi: 10.3934/krm.2021034
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

Glassey-Strauss representation of Vlasov-Maxwell systems in a Half Space

 1 Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA 2 Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53717, USA 3 Department of Mathematical Sciences, Seoul National University, Seoul 08826, Republic of Korea

This paper is dedicated to the memory of the late Bob Glassey

Received  June 2021 Early access November 2021

Fund Project: CK is supported in part by National Science Foundation under Grant No. 1900923 and the Brain Pool program (NRF-2021H1D3A2A01039047) of the Ministry of Science and ICT in Korea

Following closely the classical works [5]-[7] by Glassey, Strauss, and Schaeffer, we present a version of the Glassey-Strauss representation for the Vlasov-Maxwell systems in a 3D half space when the boundary is the perfect conductor.

Citation: Yunbai Cao, Chanwoo Kim. Glassey-Strauss representation of Vlasov-Maxwell systems in a Half Space. Kinetic & Related Models, doi: 10.3934/krm.2021034
References:

show all references

References:
 [1] Sergiu Klainerman, Gigliola Staffilani. A new approach to study the Vlasov-Maxwell system. Communications on Pure & Applied Analysis, 2002, 1 (1) : 103-125. doi: 10.3934/cpaa.2002.1.103 [2] Toan T. Nguyen, Truyen V. Nguyen, Walter A. Strauss. Global magnetic confinement for the 1.5D Vlasov-Maxwell system. Kinetic & Related Models, 2015, 8 (1) : 153-168. doi: 10.3934/krm.2015.8.153 [3] Mohammad Asadzadeh, Piotr Kowalczyk, Christoffer Standar. On hp-streamline diffusion and Nitsche schemes for the relativistic Vlasov-Maxwell system. Kinetic & Related Models, 2019, 12 (1) : 105-131. doi: 10.3934/krm.2019005 [4] Toan T. Nguyen, Truyen V. Nguyen, Walter A. Strauss. Erratum to: Global magnetic confinement for the 1.5D Vlasov-Maxwell system. Kinetic & Related Models, 2015, 8 (3) : 615-616. doi: 10.3934/krm.2015.8.615 [5] Jin Woo Jang, Robert M. Strain, Tak Kwong Wong. Magnetic confinement for the 2D axisymmetric relativistic Vlasov-Maxwell system in an annulus. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2021039 [6] Robert Glassey, Stephen Pankavich, Jack Schaeffer. Separated characteristics and global solvability for the one and one-half dimensional Vlasov Maxwell system. Kinetic & Related Models, 2016, 9 (3) : 455-467. doi: 10.3934/krm.2016003 [7] Stephen Pankavich, Nicholas Michalowski. Global classical solutions for the "One and one-half'' dimensional relativistic Vlasov-Maxwell-Fokker-Planck system. Kinetic & Related Models, 2015, 8 (1) : 169-199. doi: 10.3934/krm.2015.8.169 [8] Mihai Bostan, Thierry Goudon. Low field regime for the relativistic Vlasov-Maxwell-Fokker-Planck system; the one and one half dimensional case. Kinetic & Related Models, 2008, 1 (1) : 139-170. doi: 10.3934/krm.2008.1.139 [9] H. M. Yin. Optimal regularity of solution to a degenerate elliptic system arising in electromagnetic fields. Communications on Pure & Applied Analysis, 2002, 1 (1) : 127-134. doi: 10.3934/cpaa.2002.1.127 [10] Jörg Weber. Confined steady states of the relativistic Vlasov–Maxwell system in an infinitely long cylinder. Kinetic & Related Models, 2020, 13 (6) : 1135-1161. doi: 10.3934/krm.2020040 [11] Yemin Chen. Smoothness of classical solutions to the Vlasov-Maxwell-Landau system near Maxwellians. Discrete & Continuous Dynamical Systems, 2008, 20 (4) : 889-910. doi: 10.3934/dcds.2008.20.889 [12] Shuangqian Liu, Qinghua Xiao. The relativistic Vlasov-Maxwell-Boltzmann system for short range interaction. Kinetic & Related Models, 2016, 9 (3) : 515-550. doi: 10.3934/krm.2016005 [13] Wei Dai, Daoyuan Fang, Chengbo Wang. Lifespan of solutions to the Strauss type wave system on asymptotically flat space-times. Discrete & Continuous Dynamical Systems, 2020, 40 (8) : 4985-4999. doi: 10.3934/dcds.2020208 [14] Jingbo Dou, Ye Li. Liouville theorem for an integral system on the upper half space. Discrete & Continuous Dynamical Systems, 2015, 35 (1) : 155-171. doi: 10.3934/dcds.2015.35.155 [15] Weiwei Zhao, Jinge Yang, Sining Zheng. Liouville type theorem to an integral system in the half-space. Communications on Pure & Applied Analysis, 2014, 13 (2) : 511-525. doi: 10.3934/cpaa.2014.13.511 [16] Sufang Tang, Jingbo Dou. Quantitative analysis of a system of integral equations with weight on the upper half space. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021171 [17] Renjun Duan, Shuangqian Liu, Tong Yang, Huijiang Zhao. Stability of the nonrelativistic Vlasov-Maxwell-Boltzmann system for angular non-cutoff potentials. Kinetic & Related Models, 2013, 6 (1) : 159-204. doi: 10.3934/krm.2013.6.159 [18] Yuanjie Lei, Huijiang Zhao. The Vlasov-Maxwell-Boltzmann system near Maxwellians with strong background magnetic field. Kinetic & Related Models, 2020, 13 (3) : 599-621. doi: 10.3934/krm.2020020 [19] Chenxi Guo, Guillaume Bal. Reconstruction of complex-valued tensors in the Maxwell system from knowledge of internal magnetic fields. Inverse Problems & Imaging, 2014, 8 (4) : 1033-1051. doi: 10.3934/ipi.2014.8.1033 [20] Claude Elbaz. Gravitational and electromagnetic properties of almost standing fields. Discrete & Continuous Dynamical Systems - B, 2012, 17 (3) : 835-848. doi: 10.3934/dcdsb.2012.17.835

2020 Impact Factor: 1.432